@Abhishek De
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In this case p and q both are primes to be more specific the numbers p and q need to be co prime) so there is no question about this assumption being correct as 13 and 7 are undoubtedly co prime.

The statement n5−5 is divisible by 91 can be inferred as n5≡5(mod7) as well as(mod13). By a direct check, modulo 7, n = 3 is the only value satisfying n5≡5. So n≡3(mod7). Similarly, n≡5(mod13). By the Chinese Remainder Theorem, these two conditions are equivalent to saying that n≡31(mod91). Therefore the least 3 digit possible value of n=91×1+31=122